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x+(1/x)
Solving integrals/ x+(1/x)

Integral of x+(1/x) dx

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The solution

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∫01(x+1x) dx\int\limits_{0}^{1} \left(x + \frac{1}{x}\right)\, dx 
Integral(x + 1/x, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

    1. The integral of 1x\frac{1}{x} is log⁡(x)\log{\left(x \right)}.

    The result is: x22+log⁡(x)\frac{x^{2}}{2} + \log{\left(x \right)}

  2. Add the constant of integration:

    x22+log⁡(x)+constant\frac{x^{2}}{2} + \log{\left(x \right)}+ \mathrm{constant}

The answer is:

x22+log⁡(x)+constant\frac{x^{2}}{2} + \log{\left(x \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(x+1x) dx=C+x22+log⁡(x)\int \left(x + \frac{1}{x}\right)\, dx = C + \frac{x^{2}}{2} + \log{\left(x \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-1000010000
Plot the graph f(x)
The answer [src] 
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∞\infty 
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Numerical answer [src] 
44.5904461339929
44.5904461339929
The graph
Integral of x+(1/x) dx

    Use the examples entering the upper and lower limits of integration.

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